Internal problem ID [10446]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 2, Second order linear equations. Section 2.3.1 Nonhomogeneous Equations:
Undetermined Coefficients. Exercises page 110
Problem number: 2(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+7 x-t \,{\mathrm e}^{3 t}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve(diff(x(t),t$2)+7*x(t)=t*exp(3*t),x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (\sqrt {7}\, t \right ) c_{2} +\cos \left (\sqrt {7}\, t \right ) c_{1} +\frac {\left (8 t -3\right ) {\mathrm e}^{3 t}}{128} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 42
DSolve[x''[t]+7*x[t]==t*Exp[3*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{128} e^{3 t} (8 t-3)+c_1 \cos \left (\sqrt {7} t\right )+c_2 \sin \left (\sqrt {7} t\right ) \\ \end{align*}